Worksheet to accompany Exponential Growth and Decay stations game

Name:_______________Date:________

Exponential Growth and Decay Station GameStation 1

(a) What fraction of the original piece is left after the first tear?

(b) What fraction of the original piece is left after the second tear?

(c) Fill in the table:Number of times cut 0 1 2 3 4

Fraction of original piece left

(d) Write an expression for the fraction of the paper left after t cuts.

(e) If you continue this process, will the paper ever disappear?

Station 2(a) Fill in the table:

Number of iterations 0 1 2 3

Number of identical triangles

1

(b) Write an expression for the number of triangles after n iterations

(c) Fill out the table:Number of iterations 0 1 2 3

Triangle side length 8 inches

(d) Write an expression for the length of the side of a triangle after n iterations

Station 3(a) Fill in the table:

Number of iterations 0 1 2 3 4 5

Number of TOTAL triangles (big and

1 5

small)(b) Write an expression for the number of triangles after n iterations

(c) Is this exponential growth? Explain.

Station 4(a) Fill in the table:

Number of iterations 0 1 2 3 4 5

Number of new circles drawn

1

(b) Write an expression for the number of new circles drawn after n iterations

(c) How many new circles will you need to draw in the 10th iteration?

Station 5(a) Fill in the table:

Number of times all heads have been cut off

0 1 2 3 4 5

Number of total heads 7 14

(b) Write an expression for the number of total heads that the Hydra will have after all its heads have been cut off n times.

(c) Write an expression for the number of total heads that the Hydra will have after h heads have been cut off.